Respuesta :
Not sure about matrix equation but this is how I answer it.
Given:
muffins = 3.50
beverage = 1.75
total number of items = 32
total cost = 87.50
m + b = 32
3.50m + 1.75b = 87.50
m = 32 - b
3.50(32-b) + 1.75b = 87.50
112 - 3.50b + 1.75b = 87.50
-3.50b + 1.75b = 87.50 - 112
-1.75b = -24.50
b = -24.50 / -1.75
b = 14
m = 32 - b
m = 18
The class bought 18 muffins and 14 beverages.
3.50m + 1.75b = 87.50
3.50(18) + 1.75(14) = 87.50
63 + 24.50 = 87.50
87.50 = 87.50
Given:
muffins = 3.50
beverage = 1.75
total number of items = 32
total cost = 87.50
m + b = 32
3.50m + 1.75b = 87.50
m = 32 - b
3.50(32-b) + 1.75b = 87.50
112 - 3.50b + 1.75b = 87.50
-3.50b + 1.75b = 87.50 - 112
-1.75b = -24.50
b = -24.50 / -1.75
b = 14
m = 32 - b
m = 18
The class bought 18 muffins and 14 beverages.
3.50m + 1.75b = 87.50
3.50(18) + 1.75(14) = 87.50
63 + 24.50 = 87.50
87.50 = 87.50
Answer:
(a) [tex]\begin{bmatrix} 1 &1 \\ 2 & 1\end{bmatrix}\cdot\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}32\\ 50\end{bmatrix}[/tex]
(b) determinant of the matrix is: -1
(c) number of muffins purchased=18
number of beverages purchased=14.
Step-by-step explanation:
(a) let us assume that the number of muffins purchased=x
number of beverage purchased=y
as a class purchased a total of 32 items that means x+y=32
amount spent=$87.50 that means 3.50x+1.75y=87.50
which could also be written as: 2x+y=50
now in matrix form it could be represented as:
[tex]\begin{bmatrix} 1 &1 \\ 2 & 1\end{bmatrix}\cdot\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}32\\ 50\end{bmatrix}[/tex]
(b) the determinant of the matrix[tex]\begin{bmatrix} 1 &1 \\ 2 & 1\end{bmatrix}[/tex] is given by [tex]1\times1-2\times1=1-2=-1[/tex]
hence the determinant of the matrix is: -1
(c) now on solving the matrix we need to apply row operations in it to make it a upper triangular matrix so that it would be easy for us to calculate the value of x and y.
[tex]\begin{bmatrix} 1 &1 \\ 2 & 1\end{bmatrix}\cdot\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}32\\ 50\end{bmatrix}[/tex]
we multiply row 1 by 2 and subtract row 2 from it to get
[tex]\begin{bmatrix} 1 &1 \\ 0 & 1\end{bmatrix}\cdot\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}32\\ 14\end{bmatrix}[/tex]
on using the backward substitution in the matrix we get y=14
and x=18
Hence, number of muffins purchased=18
number of beverages purchased=14.
